The feds say a reputed Columbo-family mobster would be playing right into their hands if he goes ahead with plans to use the sympathy card with jurors at his extortion trial next week by reminding them he spent 22 years behind bars for a rape he didn’t commit.

In a letter to Manhattan federal Judge Kevin Castel, Manhattan US Attorney Preet Bharara said Friday that the government “does not object” to jurors learning that Scott Fappiano became a poster boy for DNA-crime-scene testing in 2006 when he was cleared in the rape of a cop’s wife after more than two decades in jail.

That’s likely because the government intends to seek admission as evidence a secretly taped recording in which Fappiano discusses the wrongful incarceration because the recordings shed light on the crimes for which he will stand trial Jan. 21.

The feds allege Fappiano, 52, of Staten Island, and more than 30 other reputed mobsters banded together to orchestrate a massive gangland effort to control the New York-New Jersey garbage-carting industry.

“The government believes these facts are relevant because they contextualize other discussions in the recordings [including] . . . Fappiano’s reputation and . . . standing with respect to various organized crime families,” Bharara wrote.

He also said both his office and Fappiano’s lawyers have agreed not to get into the intimate details at trial of the gruesome rape of which Fappiano was wrongly convicted, and that he opposes Fappiano’s camp bringing up his so-called “fear of police” during direct examination.